To enhance the throughput of the mobile edge computing (MEC) system, this paper investigates a rate splitting multiple access (RSMA)-MEC system assisted by a collaborative combination of the active reconfigurable intelligent surface (RIS) and the decode-and-forward (DF) relay. In this system, the active RIS is deployed to improve the signal transmission condition, while the DF relay is employed to extend the communication range. Additionally, the RSMA protocol is utilized to enhance the spectrum efficiency in multi-user access scenario, and both the relay and the base station (BS) apply the successive interference cancellation technique to decode the transmitted signals. To maximize the system throughput, the joint optimization problem involving the relay’s decoding order and transmitting power, the BS’s receiving beamforming and decoding order, the active RIS reflection coefficients, and the users’ offloading strategies are investigated. An alternating optimization algorithm is proposed to obtain the suboptimal solution for the throughput maximization problem. Finally, numerical results validate that the collaborative assistance of the active RIS and the DF relay can effectively enhance the throughput performance of the RSMA-MEC system.